a bank opens with $4.05 in nickels and pennies. There are 157 coins in total. how many nickels and how many pennies

X = The # of nickels.

(157 - X) = The # of pennies.

5X + 1(157-X) = 405 Cents.
5X + 157 - X = 405,
4X = 405 - 157 = 248,
X = 62 Nickels.
157 - X = 157 - 62 = 95 Pennies.

To solve this problem, we can use algebra. Let's assign variables to the number of nickels and pennies.

Let's say the number of nickels is represented by 'N' and the number of pennies by 'P.'

From the problem statement, we know two things:

1. The total value of the coins is $4.05.
2. The total number of coins is 157.

We can create two equations based on this information:

Equation 1: N + P = 157 (since the total number of coins is 157)
Equation 2: 0.05N + 0.01P = 4.05 (since the total value of the coins is $4.05, where a nickel is worth $0.05 and a penny is worth $0.01)

Now, we have a system of two equations with two variables. We can solve it using algebraic methods, such as substitution or elimination.

Let's use the substitution method:
From Equation 1, we can express N in terms of P:
N = 157 - P

Now substitute this expression for N in Equation 2:
0.05(157 - P) + 0.01P = 4.05

Simplify and solve for P:
7.85 - 0.05P + 0.01P = 4.05
0.01P - 0.05P = 4.05 - 7.85
-0.04P = -3.8
P = (-3.8) / (-0.04)
P = 95

Now substitute the value of P back into Equation 1 to find N:
N + 95 = 157
N = 157 - 95
N = 62

So, the bank has 62 nickels and 95 pennies.